As a practical discriminative approach to pattern classifier design, the Minimum Classification Error (MCE) training method has been extensively used. In it, classification correctness is represented by a misclassification measure whose positive value corresponds to misclassification and whose negative value corresponds to correct classification. The amount of its negative value is considered to bring in high robustness to unseen pattern samples. However, this effect of the misclassification measure on robustness increase has been questioned in recent studies. In this paper, we clarify the cause of the measure's insufficiency and propose a solution by developing a new MCE training method using geometric margin as the misclassification measure. To maintain the high application generality of the MCE framework, we derive the geometric margin for a general class of discriminant functions and demonstrate the utility of our new MCE method by installing the newly formulated general geometric margin to widely used prototype-based discriminant functions.